{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CS189/289A HW3 code part 1\n",
    "### Yicheng Chen\n",
    "### 02/15/2017\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Q2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.38905609893065"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.interpolate\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def gaussian_2d(miu, cov, x, y):\n",
    "    pi=3.1415926\n",
    "    pos = np.array([x, y])\n",
    "    S = np.linalg.det(cov)\n",
    "    C = np.linalg.inv(cov)\n",
    "    g = 1/(2*pi*math.sqrt(S)) * math.exp(-0.5*(pos-miu).dot(C.dot(pos-miu)))\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZAEPt6zkUlm2E//4FXztUzrWo0OS8SOPbXRwK2rl4TzzxLOYvTnOKZ6hBM57H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Wf48Jfw9CzA+vWXWL36PAcPhpKebqJ4cXd69KhAqVIeikzrtLUVRVkb9sCHQ827tk6CV11gXix8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec32dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a\n",
    "xi, yi = np.linspace(-1, 3, 100), np.linspace(-1, 3, 100)\n",
    "xi, yi = np.meshgrid(xi, yi)\n",
    "miu = np.array([1, 1])\n",
    "cov = np.array([[1, 0], [0, 2]])\n",
    "z = np.array([gaussian_2d(miu, cov, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "CS = plt.contour(z, extent=[xi.min(), xi.max(), yi.min(), yi.max()])\n",
    "plt.clabel(CS, inline=1, fontsize=10)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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X4NlB0K6ZffLK1iDUCdZkyM4CkB0Fw/zkVsJnF2QbmE2Dndlyet33KfBjvjFRB0/75FUQ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\nTdM0TdMAnRRomqZpmuby/0W7J+EFhnBNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f634dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b\n",
    "xi, yi = np.linspace(-3, 1, 100), np.linspace(0, 4, 100)\n",
    "xi, yi = np.meshgrid(xi, yi)\n",
    "miu = np.array([-1, 2])\n",
    "cov = np.array([[2, 1], [1, 3]])\n",
    "z = np.array([gaussian_2d(miu, cov, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "CS = plt.contour(z, extent=[xi.min(), xi.max(), yi.min(), yi.max()])\n",
    "plt.clabel(CS, inline=1, fontsize=10)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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L8/ysWVTr0MFte/RzikzvRFg8CU7sgS+3wt1mBzJDT4aYF8BQVM3w5NDPVEdn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\nfrmHTp2q5/s6SSnw0OswdRE8OgA+fvZ8IyR7RKXBbUfACqypLhn9wrU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110db25c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# c\n",
    "xi, yi = np.linspace(-3, 5, 100), np.linspace(-3, 5, 100)\n",
    "xi, yi = np.meshgrid(xi, yi)\n",
    "miu1 = np.array([0, 2])\n",
    "cov1 = np.array([[2, 1], [1, 1]])\n",
    "z1 = np.array([gaussian_2d(miu1, cov1, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "miu2 = np.array([2, 0])\n",
    "cov2 = np.array([[2, 1], [1, 1]])\n",
    "z2 = np.array([gaussian_2d(miu2, cov2, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "CS = plt.contour(z1-z2, extent=[xi.min(), xi.max(), yi.min(), yi.max()])\n",
    "plt.clabel(CS, inline=1, fontsize=10)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/N5KyV5QD8i0syr2bJHOJOFrREk88aU4zBjOQZJKJIKLgffcCR3OaUY1qnCCS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\nkr8QQgjhYCT5CyGEEA7m/wFLyHccEmPAsQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a541198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# d\n",
    "xi, yi = np.linspace(-3, 5, 100), np.linspace(-3, 5, 100)\n",
    "xi, yi = np.meshgrid(xi, yi)\n",
    "miu1 = np.array([0, 2])\n",
    "cov1 = np.array([[2, 1], [1, 1]])\n",
    "z1 = np.array([gaussian_2d(miu1, cov1, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "miu2 = np.array([2, 0])\n",
    "cov2 = np.array([[2, 1], [1, 3]])\n",
    "z2 = np.array([gaussian_2d(miu2, cov2, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "CS = plt.contour(z1-z2, extent=[xi.min(), xi.max(), yi.min(), yi.max()])\n",
    "plt.clabel(CS, inline=1, fontsize=10)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fw+9fw89pakJh+6uhx43Qvr+6iagqNAuETwFLS8i7HRw7IeoLKecsqiyPJX9N0zRgBvCL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ebdb048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# c\n",
    "xi, yi = np.linspace(-3, 5, 100), np.linspace(-3, 5, 100)\n",
    "xi, yi = np.meshgrid(xi, yi)\n",
    "miu1 = np.array([1, 1])\n",
    "cov1 = np.array([[2, 0], [0, 1]])\n",
    "z1 = np.array([gaussian_2d(miu1, cov1, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "miu2 = np.array([-1, -1])\n",
    "cov2 = np.array([[2, 1], [1, 2]])\n",
    "z2 = np.array([gaussian_2d(miu2, cov2, x, y) for (x,y) in zip(xi.ravel(), yi.ravel())]).reshape(xi.shape)\n",
    "CS = plt.contour(z1-z2, extent=[xi.min(), xi.max(), yi.min(), yi.max()])\n",
    "plt.clabel(CS, inline=1, fontsize=10)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Q3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7r+Po0XtZWbmF9CygV3PkyF2ltFPq1tLSElNTUwBTMcalfl4r1+mTQwivBq4E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\npBSDA0mSlPL/A4kSssscxkXYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4f83c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import normal\n",
    "X1 = normal(3, 3, 100)\n",
    "X2 = normal(4, 2, 100)\n",
    "X2 += X1/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: \n",
      " [ 3.55073982  5.84907657]\n"
     ]
    }
   ],
   "source": [
    "miu = np.array([X1.mean(), X2.mean()])\n",
    "print(\"Mean: \\n\", miu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance: \n",
      " [[ 9.53074878  5.16187852]\n",
      " [ 5.16187852  6.99366966]]\n"
     ]
    }
   ],
   "source": [
    "X = np.vstack((X1, X2))\n",
    "cov = np.cov(X)\n",
    "print(\"Covariance: \\n\", cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue: \n",
      " [ 13.57767557   2.94674287]\n",
      "Eigenvectors: (each column) \n",
      " [[ 0.78697226 -0.61698839]\n",
      " [ 0.61698839  0.78697226]]\n"
     ]
    }
   ],
   "source": [
    "w, v = np.linalg.eig(cov)\n",
    "print(\"Eigenvalue: \\n\", w)\n",
    "print(\"Eigenvectors: (each column) \\n\", v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5/ZKCDvZzJ5xwUp5ztuR/AXH9+vVuwYIFGUtA2X6bSNdLTvVBUFU1wo0cOUqh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\nAjrghUpQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec4e400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = v[:, 0].dot(w[0])\n",
    "v2 = v[:, 1].dot(w[1])\n",
    "\n",
    "plt.scatter(X1, X2)\n",
    "plt.xlim([-15,15])\n",
    "plt.ylim([-15,15])\n",
    "ax = plt.axes()\n",
    "ax.set_aspect('equal')\n",
    "ax.arrow(miu[0], miu[1], v1[0], v1[1], head_width=1, head_length=1, fc='g', ec='g')\n",
    "ax.arrow(miu[0], miu[1], v2[0], v2[1], head_width=1, head_length=1, fc='r', ec='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FaI/x8Yny0U7lRGr1NfVOcTKzfwQX6pLeK+l+SU9KOixpS4tlCfWcxR1O79+/P5Ww6KQm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\nASHUASAghDoABIRQB4CAEOoAEJD/D06HPYMRwPqeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec2e940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X1c = X1 - miu[0]\n",
    "X2c = X2 - miu[1]\n",
    "Xr = v.T.dot(np.array([X1c, X2c]))\n",
    "plt.scatter(Xr[0, :], Xr[1, :])\n",
    "plt.xlim([-15,15])\n",
    "plt.ylim([-15,15])\n",
    "ax = plt.axes()\n",
    "ax.set_aspect('equal')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
